Supersonic axial turbines have attracted interest in the industry since the 1950s due to the high power they provide, allowing a reduction in the number of low-pressure stages, and thus leading to lighter turbines as well as lower manufacturing and operational costs. Due to these valuable features, supersonic axial turbines are currently widely used in different power generation and mechanical drive fields such as rocket engine turbopumps [1, 2, 3, 4], control stages in high pressure multi-stage steam turbines, standalone single stage and 2-row velocity compound steam turbines [5, 6], ORC turbo-generator including geothermal binary power stations [7, 8, 9, 10], turbochargers for large diesel engines  and other applications. Therefore it is not forgotten, but instead a very important field in turbomachinery when highest specific power, compactness, low weight, low cost and ease of maintenance are dominant requirements. Especially nowadays, when development of small capacity reusable low-cost rocket launchers, compact and powerful waste heat recovery (WHR) units in the automotive industry, distributed power generation, and other fields are in extreme demand.
Typically, supersonic turbine consists of supersonic nozzles with a subsonic inlet and one or two rows of rotating blades. The turbine usually has partial arc admission. The total flow could go through either a single partial arc or several ones. The latter is typical for a steam turbine control stage or standalone applications. The inlet manifold or nozzles chests, as well as exhaust duct, are critical parts of the turbine as well. Due to the very frequent application of partial admission, it is not possible to implement any significant reaction degree. Thus, this kind of turbine is almost always an impulse type. However, some reaction degree could still be applied to full admission turbines. The influence of the rotor blades profile designed for high reaction degree on rotor-stator supersonic interaction and turbine performance is not well studied at the moment.
It is important to note that resultant simplicity of a supersonic turbine does not reflect the extremely complex approach required to design a turbine which meets design performance with high accuracy as well as capability to estimate off-design performance with the same extreme accuracy. Unfortunately, such a high accuracy approach does not exist. The accuracy of simplified design procedures available may be acceptable for some preliminary estimations, but not sufficient to guaranty a performance of the designed turbine with a reasonable degree of accuracy at design conditions and especially at off-design conditions. The reason for this situation is that the formalization of the entire complex of supersonic turbine peculiarities is a very complex task which requires significant efforts, either by comprehensive experimental investigation or by CFD calculations. Experimental tests are very expensive and require very sophisticated measurement equipment to study the different aspects which influence supersonic turbine performance in detail. Among them are partial admission, precise energy losses estimation in nozzles at design and off-design modes, active blades power production and inactive blades power consumption, supersonic rotor-stator interaction, radial gap leakages in active and inactive segments of the rotor disks including related instabilities, shroud and disk friction power, inlet manifold or nozzle chests pressure losses, exhaust duct pressure losses, axial forces and radial forces. It is almost impossible to develop an experimental facility which enables studying of all the above mentioned factors and their influence on a turbine performance. In turn, a CFD approach makes it possible to do this, but the calculation task has to be formulated very thoroughly, to take into account all of the aforementioned factors and be sufficiently accurate.
The above creates in a need for a design process which results in a simple, compact, and reliable supersonic turbine. A very promising approach is the Response Surface methods, such as DoE or neural networks. However Response Surface requires a substantial amount of source data (values for all crucial parameters for a variety of supersonic turbine configurations) which could be generated utilizing modern CFD approaches. In turn, this demands for a procedure which allows the designer to quickly generate different configurations of an entire supersonic turbine, including single stage and two row velocity compound. Examples of the automatically generated solid models of a supersonic turbines and respective fluid volumes are shown in Figure 1. The presented geometry of inlet manifold, nozzles, blade profiles, shrouds, disks, axial and radial clearances and other turbine geometry parameters are generated automatically according to a specific set of boundary conditions and fluid properties.
Such a procedure make it possible to perform a sufficient amount of numerical investigation and utilizing DoE theory or neural networks to eventually build a highly accurate mathematical model of the supersonic turbine, covering all mentioned in the beginning of this article applications. SoftInWay would be glad to discuss any further ideas and thoughts in regards to this topic with anyone who desires to design or estimate the performance of the supersonic turbine. Please feel free to shoot us an email at Info@softinway.com!
- J. Glassman, Turbine Design and Application, NASA SP-290, 1972
- Liquid Rocket Engine Turbines, NASA Space Vehicle Design Criteria, NASA SP-8110, 1974
- K. Huzel and D. H. Huang, Modern Engineering For Design of Liquid-propellant Rocket Engines, Progress in Astronautics and Aeronautics Volume 147, AIAA, 1992
- Wahle, The aerodynamic design and testing of a supersonic turbine for rocket engine application, In: Proceeding of the 3rd European Conference on turbomachinery, London, United Kingdom, 1999
- Leyzerovich, Steam turbines for modern fossil-fuel power plants, The Fairmont Press, 2008
- R. Wakeley, The Optimization of Steam turbine Design, Thesis for the degree of Doctor of Philosophy, Engineering Design Centre, University of Newcastle upon Tyne, 1997
- P. Czapla, Investigation of Supersonic Impulse Turbines for Application to Geothermal Binary Power Stations, Thesis for the degree of Doctor of Philosophy, School of Mechanical and Mining Engineering, University of Queensland, 2015
- Vernau, G. Verdonik, T. Dufournet, Supersonic turbines for Organic Fluid Rankine Cycles from 3 to 1000 kW, Development of a Supersonic Steam Turbine with a Single Stage Pressure Ratio of 200 for Generator and Mechanical Drive, von Karman Institute Lecture Series on “Small High Pressure Ratio Turbines”, 1987
- S. Kunte, J. R. Seume, Experimental Setup of a Small Supersonic Turbine for an Automotive ORC Application Running with Ethanol, 3rd International Seminar on ORC Power Systems, October 12-14, 2015, Brussels, Belgium
- R. Seume, M. Peters, H. S. Kunte, Design and Test of a 10 kW ORC supersonic turbine generator, 1st International Seminar on Non-Ideal Compressible-Fluid Dynamics for Propulsion and Power, IOP Conf. Series: Journal of Physics: Conf. Series 821, 2017
- Gronman, T. Turunen-Saaresti, A. Jaatinen, J. Backman, Numerical modeling of a supersonic axial turbine stator. J. Term Sci. 1003-2169, 2010
- Paniagua, M.C. Iorio, N. Vinha, J. Sousa, Design and Analysis of Pioneering High Supersonic Axial Turbines